The interaction between colloids in polar mixtures above Tc

0.45 MB·English

by  Sela Samin

The interaction between colloids in polar mixtures above T
c
Sela Samin and Yoav Tsori
Department of Chemical Engineering and The Ilse Katz Institute for Nanoscale Science and Technology,
Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel.
(Dated: January 18, 2012)
We calculate the interaction potential between two colloids immersed in an aqueous mixture
containing salt near or above the critical temperature. We find an attractive interaction far from
the coexistence curve due to the combination of preferential solvent adsorption at the colloids’
surface and preferential ion solvation. We show that the ion-specific interaction strongly depends
on the amount of salt added as well as on the mixture composition. Our results are in accord with
recent experiments. For a highly antagonistic salt of hydrophilic anions and hydrophobic cations,
a repulsive interaction at an intermediate inter-colloid distance is predicted even though both the
electrostatic and adsorption forces alone are attractive.
I. INTRODUCTION teraction and sometimes other specific interactions with
the polar solvent strongly depends on the solvent and
2
1 Chargedsurfacesinliquidmediaareubiquitousinsoft the chemical nature of the ion [16–18]. The total solva-
0 matter and the interaction between such surfaces has tion energy of an ion when it is transfered from one sol-
2 been studied extensively. In the seminal theory of Der- vent into another (the Gibbs transfer energy) is in many
n jaguin,Landau,Verwey,andOverbeek(DLVO)thetotal cases much larger than the thermal energy, especially if
a interaction potential is the additive combination of the one solvent is water and the other is an organic solvent
J attractive van der Waals interaction and an electrostatic [17–19]. In addition, for a given solvent, the solvation
7 repulsivescreenedCoulombpotential[1,2]. IntheDLVO energy of cations and anions is generally different due to
1 theory the liquid between the surfaces is a homogeneous theirdifferentsizeandspecificchemicalinteractionswith
dielectric medium and only enters the electrostatic po- the solvent, such as Lewis acid-base interaction. Thus,
t] tentialthroughitspermittivityε. Thesituationisdiffer- themagnitudeandsometimeseventhesignoftheGibbs
of entinsolventmixtures,wherethestructureofthesolvent transfer energy for cations and anions may differ in var-
s mayvaryinspaceduetogradientsinelectricfieldandion ious salts and solvents [19, 20].
t. density. Several authors explored experimentally the in- In bulk binary mixtures, the addition of salt modifies
a teraction between charged surfaces in mixtures [3–7]. In the coexistence curve [21–25]. When a salt-containing
m
a homogeneous binary mixture of water and 2,6-lutidine mixture is confined between charged surfaces, the influ-
- close to the demixing temperature, a reversible floccu- ence of ionic solvation on the surface interaction in mis-
d
n lation of suspended colloids has been observed [3]. The cible solvents has been studied in Ref. 15, while for par-
o flocculated region in the phase diagram is suppressed by tially miscible mixtures close to the coexistence curve it
c the addition of salt [4]. These experiments were inter- was explored in Ref. 10. In the latter case it was shown
[ preted in terms of the preferential adsorption of one of thatpreferentialsolvationalonecanqualitativelymodify

1 thesolventsonthecolloidsurfaceinaccordwithwetting the interaction between similarly charged surfaces, re-
v theory[8,9]. Morerecently,itwassuggestedthatthese- sulting in a strong long-range attraction.
5 lective solvation of ions in the two solvents is important Inordertoaccountfortherecentexperimentalfindings
3 in these experiments [10, 11] as well as charge-regulation in critical mixtures [7], Bier et. al. [13] had employed a
5 effects [11]. lineartheorythatincludesbothionsolvationandsolvent
3
Recently,directmeasurementoftheinteractionpoten- adsorptionontheconfiningsurfaces. Recently, Okamoto
.
1 tial between a colloid and a charged wall was performed and Onuki [11] also included in the theory solvent de-
0 in water–2,6-lutidine mixtures below the lower critical pendent charge-regulation, and studied the interaction
2 solution temperature (LCST) [6, 7]. In these experi- induced by prewetting and wetting transitions close to
1
ments the addition of salt greatly influenced the range the coexistence curve.
:
v and strength of the interaction [7], leading to an attrac- Inthispaperwetheoreticallyinvestigatehowtheinter-
Xi tiveinteractionfarfromthecriticaltemperatureTc. Ad- playbetweenionsolvationandsolventadsorptionaffects
ditionofsalthasaremarkableeffectontheflocculationof theinteractionbetweensurfacesinthenonlinearregime.
r
a colloids in a critical mixture of water–3-methylpyridine, We show that a strong attraction exists even far from
where it reduces dramatically the onset temperature of T due to the nonlinear coupling between solvation and
c
theflocculation[5]. Preliminaryexperiments[12]suggest adsorption. These effects are strongly ion-specific and
that the variation of the mixture composition also has a hence depend on the salt properties and concentration.
pronounced effect on the interaction. We highlight the qualitative features of the theory and
Atheoreticalefforthasbeenmadetoincorporateionic give several new predictions.
solvation effects in polar mixtures [10, 11, 13–15]. The We focus on the regime far from the prewetting and
solvation energy of an ion arising from the ion-dipole in- wettingtransitionsandneglectcharge-regulation,assum-
2
ing large surface ionization. Thus, we do not expect any isproportionaltothecoefficients∆u+ and∆u forposi-
−
discontinuitiesinphysicalquantitiessuchaspressureand tive and negative ions, respectively [26]. In this form the
adsorption. We concentrate on electrostatics and ion- Gibbs transfer energies of the ions are T∆u (φ −φ ),
± 2 1
solvation forces and hence ignore the van der Waals in- where φ and φ are the compositions of two solvents.
1 2
teraction (which is relatively small in the current range Inadditiontothebulkterm,oneaddsthecontribution
(cid:82)
of parameters). oftheconfiningsurfacestothefreeenergy: F = f dS,
s s
The organization of this paper is as follows. In Sec. II where f is the surface free energy density given by:
s
wepresentacoarse-grainedmodelofasalt-containingbi-
f =eσψ +∆γφ , (3)
narymixture,takingintoaccountthespecificion-solvent s s s
and surface-solvent interactions. In Sec. III we present
where ψ and φ are the electrostatic potential and mix-
results for critical and off–critical mixture compositions s s
ture composition at the surface, respectively. Eq. (3) in-
andshowhowionspecificeffectscanbeusedtotunethe
cludes a short range interaction between the surface and
inter–colloidal potential. Conclusions are given in Sec.
liquidwhichislinearinφ,neglectinghigherorderterms.
IV.
Thesurfacefield∆γ measuresthedifferencebetweenthe
surface-water and surface-cosolvent surface tensions.
The fluid is in contact with a matter reservoir having
II. MODEL
composition φ0 and ion densities n±0. Hence, the appro-
priatethermodynamicpotentialtoextremizeisthegrand
Thesurfacesofthetwocolloidsaremodeledasparallel
potential Ω:
platesofareaS separatedbyadistanceDandcarryinga
(cid:90)
uniformchargedensityeσ andeσ perunitarea,where
L R Ω=F +F − [µφ+λ+n++λ n ]dr, (4)
eistheelementarychargeandtheindicesLandRdenote b s − −
theleftandrightplates,respectively. Anaqueousbinary
mixturecontainingsaltisconfinedbetweentheplates. φ whereµandλ±aretheLagrangemultipliersforthecom-
is the volume fraction of the water (0 ≤ φ ≤ 1), while positionandions,respectively. Theycanbeidentifiedas
thedensitiesofthepositiveandnegativeionaredenoted the chemical potentials of the species in the reservoir:
by n+ and n−, respectively. Given their low density and µ=µ0(φ0,n±0) and λ± =λ±0(φ0,n±0).
smallsize,thevolumefractionsoftheionsareneglected. Thegoverningequationsareobtainedbyminimization
For the fluid free energy we have F = (cid:82) f dr, where of Ω, leading to the Euler-Lagrange equations
b b
f is the bulk free energy density: [23, 26]
b δΩ ±eψ
= +log(v n )−∆u φ−λ =0, (5)
0 ± ± ±
f C 1 δn T
b =f (φ)+ |∇φ|2+ ε(φ)(∇ψ)2 ±
m δΩ
T 2 2T =∇·(ε(φ)∇ψ)+(n+−n )e=0, (6)
+n+(cid:0)log(v n+)−1(cid:1)+n (cid:0)log(v n )−1(cid:1) δψ −
0 − 0 −
δΩ ∂f 1 dε
−(∆u+n++∆u−n−)φ. (1) =−C∇2φ+ m − (∇ψ)2
δφ ∂φ 2T dφ
HeretheBoltzmannconstantissettounityandT isthe −∆u+n+−∆u n −µ=0. (7)
− −
thermal energy. v = a3 is the molecular volume of the
0
solvent molecules where a is the linear dimension of the The first equation yields the Boltzmann distribution for
molecules. The first term in Eq. (1) is the mixture free the ion density
energy [27]:
n± =v0−1eλ±e∓eψ/T+∆u±φ. (8)
v f =φlog(φ)+(1−φ)log(1−φ)+χφ(1−φ), (2)
0 m
Note the dependence on the mixture composition in this
where χ ∼ 1/T is the Flory interaction parameter. In equation. The ion distributions are inserted into Eq. (6)
this symmetric model the critical composition is given to obtain a modified Poisson-Boltzmann equation with
by φc =1/2. The square-gradient term in Eq. (1) takes the boundary conditions −n·∇ψL,R = eσL,R/ε. n is
into account the free energy increase due to composition the outward unit vector perpendicular to the surface.
inhomogeneities[27],whereC isapositiveconstant. The The governing equation for the composition [Eq. (7)]
third term in Eq. (1) is the electrostatic energy density, issupplementedbytheboundaryconditionsn·∇φ =
L,R
where ψ is the electrostatic potential. This energy de- ∆γ . Assuming that ψ = 0 in the reservoir, the La-
L,R
pends on the composition through the constitutive rela- grange multipliers for the different species are:
tion for the dielectric constant: ε = ε(φ). For simplicity
εweaunsde tεhearlientehaer wfoartmer: aεn(dφ)co=soεlvce+nt(pεwerm−itεtci)vφit,iewsh,erree- µ0 = ∂∂fφm(φ0)−∆u+n+0 −∆u−n−0 (9)
w c
spectively. The second line of Eq. (1) is the ideal-gas λ±0 =log(v0n±0)−∆u±φ0 (10)
entropyoftheions,validatlowdensities,whilethethird
line is the ion solvation in the mixture. In the simple bi- In our effectively one dimensional system, solution of
linearformweemploy, thestrengthofselectivesolvation the Euler-Lagrange equations yields the density profile
3
φ(z) and potential ψ(z) from which we calculate all rele-
vant quantities. Of particular interest is the pressure P
n
exerted on the surfaces by the liquid. −Pn is the normal 4 (a)
component of the Maxwell stress tensor and it is given
2
by [15, 28]:
P C ∂f T] 0
n = |∇φ|2−Cφ∇2φ+φ m −fm+n+(1−∆u+φ) [
T 2 ∂φ U −2
(cid:18) (cid:19)
1 dε
+n (1−∆u φ)− φ +ε (∇ψ)2 (11)
− − 2T dφ −4
τ =0.013
InaplanargeometryP isthezzcomponentofthestress −6 τ =0.01
n τ =0.008
tensorandisuniforminmechanicalequilibrium. Thenet τ =0.003
τ =0.002
pressure on the plates is given by the osmotic pressure −8
5 10 15 20 25 30 35 40
Π=P −P , where P is the bulk pressure. The inter-
zz b b D [nm]
action potential between the plates U(D) is calculated
from the osmotic pressure through
(b)
(cid:90) D
U(D)=−S Π(D(cid:48))dD(cid:48). (12) 0.1
∞
The excess surface adsorption in a planar geometry is 0.08
defined as usual by
Γ
1 (cid:90) D 0.06
Γ= [φ(z)−φ ]dz. (13)
0
D
0
0.04
Thisquantityismeasurableexperimentallyandaccounts
forthetotalexcessoffluidbetweentheplatesrelativeto
the bulk. 0.02
5 10 15 20 25 30 35 40
D [nm]
III. RESULTS
In the following we examine the interaction potential FIG. 1. (a) The interaction potential U(D) between two col-
U(D) for a binary mixture containing 10mM of salt at loidsatadistanceDatdifferenttemperaturesτ ≡T/Tc−1>
temperatures larger than the critical temperature, T > 0 immersed in a mixture at a critical composition (φ0 =φc).
U(D) becomes attractive as τ decreases. Here n = 10mM
T . 0
c and ∆γ = 0.1T/a2, corresponding to about 3.4 mN/m.
R,L
For the solid curves, ∆u± = 4 and the surfaces have the
same charge σ =−σ . Dash-dot curve: the same as the
A. Colloidal interaction in a mixture at a critical L,R sat
solid curve for τ = 0.008 except that σ = 3σ = −1.5σ .
composition L R sat
Dashed curve: the same as for τ =0.008 except that ∆u− =
8. (b) The corresponding excess surface adsorption Γ. In
We start with a reservoir at a critical composition, thisandinotherfigures,asanapproximationofawater–2,6-
φ = φ , confined by two hydrophilic (∆γ > 0) col- lutidine mixture we used T = 307.2K, v = 3.9×10−29m3,
0 c R,L c 0
loids. We first consider the symmetric case where both C = χ/a [27], ε2,6−lutidine = 6.9 and εwater = 79.5, and the
colloids are identical: ∆γ = ∆γ and σ = σ . We surface area is taken to be S =0.01µm2.
L (cid:112)R L R
set σ = −σ , where σ = 8n /(πl ) and l =
L,R sat sat 0 B B
e2/(4πε(φ )T) is the Bjerrum length. σ is used be-
0 sat
cause the effective surface charge saturates to this value betweenthegoverningequationsthatisresponsibletoan
in the high bare charge limit [29]. Furthermore, we as- attractive interaction far from Tc.
sumesymmetricpreferentialsolvation,i.e. ∆u+ =∆u , The solid curves of Fig. 1(a) show U(D) as a function
−
and in this case the solvation asymmetry parameter, de- ofthereducedtemperatureτ ≡T/T −1forT >T . Far
c c
fined as ∆ud ≡∆u+−∆u , vanishes: ∆ud =0. above T U(D) is purely repulsive; as the temperature
− c
The parameters we use are such that in the resulting is decreased toward T the interaction becomes attrac-
c
profilesψ(z;D)andφ(z;D)theconditionseψ(z;D)/T (cid:38) tive. The change in the shape of U(D) originates from
1 and ∆u (φ(z;D)−φ ) (cid:38) 1 hold. Hence, a lineariza- theinterplaybetweensurfacefield,thesolvationinduced
± 0
tion of Eq. (5) is not expected to be accurate [11, 13]. attraction, and the electrostatic repulsion between the
In fact, we show below that it is the nonlinear coupling plates. The attraction between the plates is stronger
4
down to τ = 0.003 and then becomes less attractive for
τ = 0.002. The attraction range of a few tenths of nm,
itsstrengthofafewT,aswellasthetemperaturedepen- 4 (a)
dencearesimilartothoseobservedinrecentexperiments
[7, 12]. 2 τ =0.009
The dashed and dash-dot curves in Fig. 1(a) are the ]
T
same as the solid curve for τ = 0.008 except for one pa- [ 0
rameter. The effect of charge asymmetry is shown by U
thedash-dotcurve, wherethetotalchargewaskeptcon-
−2
stant, but σ =3σ . Here the attraction is stronger, as
L R
in the classic Poisson-Boltzmann theory [30], since the
−4 ∆u+=4,∆u−=8,∆γL,R =0
electrostatic repulsion between surfaces is weaker for the ∆u±=0,∆γL,R =0.1Ta−2
ainsgym∆mue−trbicyc4as(e∆. uTdhe=d−as4h)edrescuulrtvseinshoawssligthhatltyinwceraekaesr- −6 5 10 ∆u1+5=4,∆20u−=82,5∆γL,R30=0.13T5a−2 40
interaction. In the linear theory [11, 13], solvation cou-
D [nm]
plingonlyentersasaterm∝∆ud. Thus, bycomparison
to the solid curve in Fig. 1(a) where ∆ud =0, it is clear
that in the nonlinear regime this type of contribution is 4 (b)

smaller than contributions proportional to ∆u .
±
TheGibbsadsorptionΓcorrespondingtothecurvesin 2 τ =0.005
Fig. 1(a) is shown in Fig. 1(b). When the surface sepa-
]
ration decreases Γ increases as the adsorbed fluid layers T
[ 0
near the walls merge. Furthermore, since the density of
U
the ions also increases, more fluid is drawn to the walls
−2
because of the solvation interaction. Γ increases as the
adsorbed fluid layer thickness, which is comparable to
the bulk correlation length, increases closer to T . −4
c
The parameters we use are close to those used in ex-
periments in a salt containing water–2,6-lutidine mix- −6
5 10 15 20 25 30 35 40
ture below the LCST [7, 12]. In these experiments it
D [nm]
is reasonable to assume that the surfaces have different
charge densities because of their different chemical na-
ture. Therefore, below we use σ = 3σ = −1.5σ
L R sat
for hydrophilic surfaces. The value of ∆γ was chosen FIG.2. Theeffectofremovingpreferentialsolvationorshort-
arbitrarily since there is no molecular theory to predict range chemical interactions on the potential U(D) between
it accurately. Furthermore, in water–2,6-lutidine mix- the colloids at temperatures given by (a) τ = 0.009 and (b)
turestheanionsareexpectedtofavorthewaterenviron- τ =0.004. Thedashedanddash-dotcurvesshowU(D)when
ment more than the cations, since 2,6-lutidine is a Lewis either the surface chemical affinity or preferential solvation
parameters are zero, respectively. In the solid curves both
base. This is supported by data of Gibbs transfer ener-
short-range chemical preference and solvation are included.
gies of ions in water-pyridine mixtures [19]. 2,6-lutidine
These two interactions are clearly non additive as the solid
is a structural analog of pyridine and hence on the basis
curve is not the sum of the dashed and dash-dotted lines.
of Ref. 19 we took ∆u+ = 4 and ∆u = 8. We stress
−
that over a wide range of values for σ and positive
L,R
∆γ , the results do not change qualitatively. This is
L,R
also true for the solvation parameters as long as the ions leads to an attractive interaction near Tc. Interestingly,
are hydrophilic, ∆u > 0. Note that the molecular vol- asisshowninFig. 2,theattractionbetweenthesurfaces
±
umes of the two components differ substantially in the is significantly altered by the coupling of solvation and
real mixture leading to φ (cid:54)=1/2. Furthermore, our sim- surface fields.
c
plifiedmodelmixturehasanuppercriticalsolutiontem- In part (a) we highlight this idea by choosing param-
perature, whereas experiments are performed below the eters such that far from T , removing either the surface
c
LCST in water–2,6-lutidine mixtures. Thus, one should tension (dashed curve) or preferential solvation (dash-
interpret results in terms of the absolute distance from dot curve) the interaction is purely repulsive. When
Tc. both forces are present the result is surprisingly a strong
U(D) can be attractive when only surface fields are attractive interaction between the colloids (solid curve).
present (∆u = 0, ∆γ (cid:54)= 0) due to critical adsorp- Fig. 2(b) shows that closer to T , an attractive interac-
± L,R c
tion [31–35]. When only preferential solvation exists tionofsimilarmagnitudeexistswheneitherforceismiss-
(∆u (cid:54)=0, ∆γ =0), wehaveshownrecently[10]that ing, but the interaction is unexpectedly much stronger
± L,R
fluid enrichment near the surface, induced by solvation, when both are present. Thus, in the nonlinear regime,
5
4
(a)

4 2
φ =0.48
2 0 T]
] 0
T [
[ U
0
U
−2
−2
τ =0.0174,κξb=0.66
−−64 5 10 15 20 ττττ ====250000....00001111654336,,,0,κκκκξξξbbbξb====30005...0677.6913840 −−64 nnn000===000...00000179MMM
5 10 15 20 25 30 35 40
D [nm]
D [nm]
(b) FIG. 4. Solid curves show the dependence of U(D) on the
4 mixture salt concentration n with ∆u+ = 4 and ∆u− = 8;
0
colloidal attraction increases with the addition of salt. The
φ =0.52
2 0 attractionisweakforasaltconcentrationofn =0.01Mbut
T] with ∆u± = 0 (dashed curve). Here φ = φ0, τ = 0.008,
0 c
[
U 0 ∆γL,R =0.1 and σL =3σR =−1.5σsat.
−2
As is seen in Fig. 3 for φ (cid:54)= φ , the curve U(D)
τ =0.009,κξb=0.86 0 c
−4 τ =0.008,κξb=0.93 becomes attractive closer to Tc, similar to the φ0 = φc
τ =0.006,κξb=1.05 case, but the temperature range at which this occurs is
−6 5 10 15 20 2τ5=0.00340,κξb3=51.2440 different. The attractive interaction is stronger for φ0 <
φ [Fig. 3 (a)] and thus the temperature range above T
D [nm] c c
atwhichitoccursislarger;comparewithτ valuesinFig.
2. NotethatinFig. 3(a)severalcurveshavemetastable
statesandthattheinteractionisrepulsiveatlongrange.
FIG. 3. Interaction potentials at different temperatures τ, The attractive interaction is weaker for φ > φ [Fig. 3
0 c
(a) for φ0 = 0.48 < φc with ∆γR,L = 0.1T/a2 and (b) for (b)]. Here, we had to use a larger value of water-surface
φ = 0.52 > φ with ∆γ = 0.4T/a2. The onset temper-
0 c R,L interactioninordertoobtainapotentialdepthsimilarto
ature for attraction is higher for φ < φ due to preferential
0 c the one which can be resolved in experiments (few T’s)
solvation. In (a), at intermediate temperatures the potential
[7].
has metastable states. Here we used ∆u+ =4, ∆u− =8 and
In order to understand the dependence on reservoir
σ =3σ =−1.5σ . Wetooktheaverageiondensitytobe
L R sat
n0 =10mM leading to κ values of κ(cid:39)2.69nm. compositionweinsertEq. (10)forλ±0 intotheBoltzmann
distribution Eq. (8) to obtain
solvationandadsorptionforcesarenonadditiveandtheir n± =n0e∓eψ/T+∆u±(φ−φ0). (14)
coupling can account for attractive interactions far from
This equation suggests that the ion density near the
T .
c plates increases when φ is reduced, which is verified nu-
0
merically. This leads to a decrease of the osmotic pres-
sure in the system since when ∆u φ > 1 the solvation
±
B. Surface interaction in an off-critical mixture
contribution to Π overcomes the ions entropic repulsion
[cf. Eq. (11)]. Thus, the coupling between the mixture
The interaction potential between two surfaces for off- composition and the ion density is important for the in-
critical mixture compositions at different temperatures teraction between the surfaces. Due to the ion-solvent
is shown in Fig. 3. The legend also shows the di- coupling the attraction is increased when salt is added.
mensionless parameter κξ corresponding to τ, where This effect is shown by the solid curves in Fig. 4 and is
√ b
κ = 8πl n is the Debye wave number and ξ is the seen in experiment [5, 12]. The dashed curve in Fig. 4
B 0 b
bulk correlation length in the absence of ions, defined as shows U(D) for the highest salt concentration but in the
(cid:112)
ξ (τ) = χa2/(∂2f (φ )/∂φ2). The combination κξ absence of ion-solvent coupling (∆u = 0). In this case
b m c b ±
is useful for comparison with experimental results. Ex- the attraction is very weak, indicating that the decrease
perimentally, it was found that ions do not modify the in Debye length when salt is added is not significant for
correlation length significantly [7]. the potential at the given parameters.
6
In general, attraction occurs up to a temperature win-
dow ∆T ≡T −T ≈5K above T , quite far from T but
c c c 2 (a)
not as large as ∆T ≈ 10K recently observed in experi-
ments. This is reasonable given the simplified mixture
model, difference in geometry and many approximations
1
of unknown quantities, e.g. σ, ∆γ, and S. Also, in ex- ]
T
periments the asymmetric binodal curve of water–2,6- [
lutidine mixtures is much ”flatter” near T compared to U 0
c
the binodal in the symmetric Flory-Huggins model we
use. τ =0.194
−1 τ =0.109
Better agreement with experiments is achieved when τ =0.048
τ =0.031
the values of κξb are compared. Attraction is observed τ =0.013
experimentally when κξ is in the range κξ ≈ 0.85−1 −2 τ =0.008
b b
5 10 15 20 25 30 35 40
forφ =φ [7]. Inpreliminaryexperimentaldata[12]we
0 c D [nm]
find κξ ≈0.65−0.8 for φ <φ and κξ ≈1.1−1.8 for
b 0 c b
φ > φ . These values are in the range of those in Fig.
0 c
2 and Fig. 3. The difference in temperature range be- 2 (b)

tween the experiments and our theory can be explained
by the different scaling of ξb =ξ0|τ|−ν. The experimen-
1
tal value of ξ and the critical exponent ν = 0.61 [7]
0 ]
are quite different from the mean field values of ξ and T
0 [
ν =0.5. Thus, the adsorbed liquid layers in experiments U 0
are thicker, leading to attraction at temperatures higher
above Tc. Nevertheless, our results qualitatively show ∆u±=4
that including ion solvation in the theory accounts for −1 ∆u+=4,∆u−=6
colloid-surface attraction far from T in salt containing ∆u+=4,∆u−=8
c ∆u+=6,∆u−=10
mixtures. −2 ∆u+=-2,∆u−=2

5 10 15 20 25 30 35 40
D [nm]
C. Interaction between hydrophilic and
hydrophobic colloids
FIG.5. IntercolloidpotentialsU(D)forhydrophilicandhy-
Another physically relevant scenario is that of hy- drophobiccolloids(antisymmetricboundaryconditions). For
drophilic and hydrophobic colloids, i.e antisymmetric the surface on the right we used ∆γR = 0.1T/a2 and σR =
short-range chemical boundary conditions. For this case −σsat. For the surface on the left we used ∆γL =−0.4T/a2
theadsorptionforceintheabsenceofsaltisrepulsive[32– and σL = −0.01σsat (cid:28) σsat. (a) The interaction potential
U(D) at different temperatures τ showing that U becomes
34]. However, experimentallyitwasobservedthatinthe
attractive when τ decreases, but repulsive close to T . Here
presenceofsalttheinteractionpotentialbecomesattrac- c
we took for the ions ∆u+ = 4 and ∆u− = 8. (b) U(D) at
tive when the temperature is decreased toward T , but
c τ = 0.048 and different values of ∆u±. The interaction is
then repulsive again as Tc is further approached [7]. In purelyrepulsivefor∆ud =∆u+−∆u− =0(dash-dotcurve)
order to explain this phenomenon, Pousaneh and Ciach and weakly attractive for ∆ud = 2 (dashed curve). The at-
[14] assumed ions that are insoluble in the cosolvent and tractionismuchstrongerinthesolidcurves,allhavingdiffer-
suggested that the attraction is due to the hydration of entvaluesof∆u±butthesamedifference∆ud =−4. Among
ions and is of entropic origin. Another explanation was these curves, the attraction is strongest for the antagonistic
given by Bier et. al. [13], who attributed the attraction salt (∆u− =−∆u+ =2).
to the difference in preferential solvation of ions ∆ud. In
their theory the attraction is linear in ∆ud.
Fig. 5 (a) shows the non-monotonous behavior of Theonsetoftherepulsiveforceisatasurfacedistance
U(D) for antisymmetric surface fields within our theo- D ≈4ξb,occurringwhenthetwoadsorbedsolventlayers
retical framework. Here we assumed the ions have dif- begin to overlap [35]. At larger surface separations, the
ferent solubilities, ∆ud = −4, and the surface charge of depletion of the more hydrophilic anions close to the hy-
thehydrophobicsurfaceismuchsmallerthanthatofthe drophobic surface gives rise also to an enhanced and en-
hydrophilic surface, as is usually the case. For these pa- ergetically favorable hydrophilic solvent depletion. The
rameters linear theory, relying on the asymmetry in the net result is an attractive interaction at D (cid:38)4ξb. As the
solvation energy of ions, reproduces surprisingly well the critical temperature is approached and ξb increases the
non-monotonous behavior [13]. In the nonlinear regime repulsiveadsorptionforcedominatesthisrelativelysmall
∆ud (cid:54)= 0 is a requisite for this trend but the interaction attraction.
dependsonthenominalvaluesof∆u asisshownbelow. Fig. 5 (b) demonstrates the influence of the value of
±
7
∆u+, ∆u , and their difference ∆ud on the interaction
−
profile U(D). In the solid blue curve we plot U(D) for
∆ud = −4 where ∆u+ = 4 as in Fig. 5 (a). Reduc- 10 (a)
tion of ∆ud from −4 to −2 (dashed curve) diminishes
the strength of interaction by an order of magnitude, a
5
strongnonlinearresponse. For∆ud =0(dash-dotcurve) ]
T
the interaction is repulsive. Fig. 5 (b) shows that the [
nominal values of ∆u+ and ∆u are important, not just U 0
−
their difference. The solid curves in this figure all have σL,R =-σsat,
∆druodph=ili−c4sabltut(pduirffpelreencturvvael,ue∆suo+f ∆=u6±).thFeoratatrmacotrieonhyis- −5 σ∆∆Luu,R++===22σ,,sa∆∆t,uu−−==44
weaker while for an antagonistic salt where the cations σL=-σR=σsat,
are hydrophobic and the anions are hydrophilic (yellow −10 ∆u+=-6,∆u−=6

curve, ∆u+ =−2) the attraction is much stronger. The 5 10 15 20 25 30 35 40
D [nm]
reasonforthisisthathydrophobiccationsreducethewa-
teradsorptiononthehighlychargedhydrophilicsurface,
thusreducingtherepulsiveadsorptionforceandamplify- 10 (b)

ing the asymmetric solvation effect. The antisymmetric
case is an example of the delicate and complex interplay 5
betweensolventadsorptionandelectrostaticinteractions
]
in confined salty mixtures. T 0
[
U
−5
D. Ion specific effects
−10 ∆γL,R =0.1Ta−2 ,∆u±=4
In this section we discuss some consequences of the ∆γL,R =-0.1Ta−2 ,∆u±=0
specific nature of the ion solvation. The ion solvation −15 ∆γL,R =-0.1Ta−2 ,∆u±=4

5 10 15 20 25 30 35 40
energy can vary greatly depending on the chemical na-
D [nm]
ture of the ion and solvent, its value being typically in
the range ∆u∼1−10T. Thus, the influence of the ion-
solventcouplingontheinteractionpotentialishighlyion-
specific. In Fig. 6 (a) we plot U(D) for hydrophilic ions FIG.6. (a)Theeffectofthesignofthecolloids’chargeonthe
and surfaces, ∆u+ =2, ∆u =4 and ∆γ =0.1T/a2. inter-colloidpotentialU(D). Theinteractionisattractivefor
− R,L
When the surfaces are both positively charged (dash-dot two positively charged surfaces and is repulsive for two neg-
curve), the anions are in excess between the plates and atively charged surfaces; compare the dash-dot and dashed
U(D)isattractivesince∆u− =4islargeenoughandthe curves. We used ∆u+ = 2, ∆u− = 4, ∆γR,L = 0.1T/a2
and τ = 0.008. In the solid curve the surfaces are both hy-
solvation-related force overcomes electrostatic repulsion.
drophilic (∆γ =0.1T/a2) but oppositely charged. For an
However, this is not the case for negatively charged sur- R,L
antagonistic salt with ∆u− =−∆u+ =6 there is a repulsive
faces(dashedcurve)whereU(D)isrepulsive. Inthiscase
regime at an intermediate range. (b) The effect of the hy-
thecationsareinexcessbetweentheplatesand∆u+ =2
drophilicty or hydrophobicity of the colloid’s surface. In the
is notlarge enoughto overcome therepulsion. Thus, the absence of preferential solvation (∆u± =0) two hydrophobic
difference in the preferential solvation of cations and an- (and hydrophilic, not shown) surfaces weakly attract (dash-
ions can produce a selective interaction with respect to dot curve). For a hydrophilic salt (∆u± = 4), hydrophobic
the sign of the surface charge. surfaces repel (solid curve) whereas hydrophilic surfaces at-
An even more intriguing scenario is that of oppositely tract (dashed curve). We used τ =0.003 and σL,R =−σsat.
chargedsurfaces,whereforhydrophilicsurfacestheinter-
action is expected to be purely attractive since both ad-
sorptionandelectrostaticforcesareattractive. Nonethe- due to hydrophobic anions. This depletion reduces the
less, if the mixture contains a strongly antagonistic salt adsorptionforceandtheoverallresultisarepulsiveinter-
(cid:12) (cid:12)
(∆u+∆u− < 0, (cid:12)∆ud(cid:12) (cid:29) 1), U(D) has a repulsive re- action. Atsmallseparationstheadsorptionlayersmerge,
gion, as is seen in the solid curve in Fig. 6 (a) for which Γ increases, and combined with the electrostatic attrac-
∆u = −∆u+ = 6. In this curve, since σ = −σ the tion the potential is strongly attractive as expected.
− R L
adsorption of both anions and cations is significant and Similar to the effect of the sign of the surface charge,
similar in magnitude. Hence, since ∆u = −∆u+ the the ion-solvent coupling renders the interaction specific
−
contribution of the solvation energy to the interaction is also relative to the sign of the surface field. In the ab-
small. In addition, at separations D (cid:38) 4ξ , prior to the sence of salt, if both surfaces are hydrophobic or hy-
b
merging of the adsorbed solvent layers [35], there is sig- drophilic they attract [31–34]. As we saw before, for hy-
nificant solvent depletion near a positively charged wall drophilicsurfacesthepreferentialsolvationofhydrophilic
8
ions greatly enhances the interaction far from T , see repulsive interactions combine to an attraction [Fig. 2
c
the dashed curve in Fig. 6 (b) for ∆u = 4 and (a)], (ii) for a hydrophilic salt, hydrophobic surfaces re-
±
∆γ =0.1T/a2. By reversing the sign of ∆γ [solid pelwhereashydrophilicsurfacesattract[Fig. 6(b)], (iii)
R,L R,L
curveinFig. 6(b)]theinteractionbecomesrepulsivefor two oppositely charged colloids repel down to distances
hydrophobicsurfacesandhydrophilicions. Thedash-dot ∼10nm and have a high repulsive barrier of 5-10T [Fig.
curve in Fig. 6 (b) shows that for hydrophobic surfaces 6 (a)], or (iv) two similarly charged colloids repel when
in the absence of preferential solvation (∆u = 0) the they are negatively charged and attract when they are
±
interaction is weakly attractive. Here, the addition of both positive [Fig. 6 (a)].
hydrophilic ions renders the interaction repulsive by re- Ourmean-fieldtheoryallowsthesemi-quantitativein-
ducing the adsorption of the solvent on the hydrophobic terpretation of recent experiments performed in salty
surface while greatly increasing the adsorption and at- mixturesnottooclosetothecriticaltemperature[7,12].
traction for hydrophilic surfaces. Wedonotlookattheinfluenceofthecriticalfluctuations
ontheinteractionbetweensurfaces[6,31–34]althoughit
has been argued that the addition of salt does not alter
IV. CONCLUSIONS the universal critical behavior of the solvent [13].
Recently, multilamellar structures were observed in a
In summary, we calculated the interaction potential bulk binary mixture upon the addition of an antagonis-
U(D)betweentwochargedcolloidsinsalt-containingbi- tic salt [36]. In light of the current work, we believe that
nary mixtures. The preferential adsorption of one of the theeffectofantagonisticsaltsontheinteractionbetween
solvents on the colloid’s surface combined with the pref- surfaces is intriguing and deserves similar attention. In
erentialsolvationoftheionsgivesrisetoastrongattrac- addition,fortemperaturesbelowthecriticaltemperature
tion between the colloids far from the coexistence curve and/or near the wetting and prewetting transitions, first
of the mixture. For surfaces with symmetric chemical ordercapillarycondensation[10]andbridgingtransitions
affinity, the interaction is governed by the individual ion [11]havebeenpredicted. Inlightofthecurrentworkand
solvation (∝ ∆u±) and to a lesser extent by the differ- these recent findings we stress the importance of prefer-
ence in solvation energies of cations and anions. This entialsolvationinsaltymixtures. SincetheGibbstrans-
is true also for the attraction for antisymmetric bound- fer energy of ions is usually larger than the thermal en-
ary conditions albeit here ∆ud (cid:54)= 0 is a requisite for an ergy, the solvation-related force can either induce large
attractive potential. composition perturbations by itself [10] or amplify them
The ion and solvent densities near the surface of the significantly if already present, as in this work.
colloid are highly sensitive to the ion solvation energy.
Thus, the bulk mixture composition φ and salt con-
0
centration n play an important role in determining the
0
ACKNOWLEDGMENTS
inter-colloid potential (Fig. 3 and Fig. 4) and this
suggests the possibility of fine-tuning the potential with
these readily controllable parameters. In addition, the We gratefully acknowledge numerous discussions with
ion specific nature of the solvation energy renders the D. Andelman, C. Bechinger, M. Bier, J. Dietrich, L.
interaction potential sensitive to the sign of the surface Helden, O. Nellen, A. Onuki and H. Orland. This work
charge or surface fields, as is shown in Fig. 6. We show was supported by the Israel Science Foundation under
that the interplay between surface and ion-specific inter- grant No. 11/10 and the European Research Council
actions may lead to non trivial effects whereby (i) two “Starting Grant” No. 259205.
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